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Exhibit 23.1

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CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the following Registration Statements on Form S-1 (333-284627, 333-286384, 333-287478, 333-288667, 333-290968, 333-293136, 333-267412 and 333-273015), Form S-3 (333-288595) and Form S-8 (333-285865, 333-258026, 333-263609, 333-270585 and 333-277994) of our report dated March 12, 2026, with respect to the financial statements of Acurx Pharmaceuticals, Inc. included in this Annual Report (Form 10-K) of Acurx Pharmaceuticals, Inc. for the year ended December 31, 2025. Our audit report includes an explanatory paragraph relating to Acurx Pharmaceuticals, Inc.’s ability to continue as a going concern.

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/s/ CohnReznick LLP

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Parsippany, New Jersey

March 12, 2026

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